Methods for stimulating the effect of distortion on representations of markers and methods for analyzing representations of markers using simulations of distortion

ABSTRACT

A method of simulating the effect of distortion on a representation of a marker, such as a fingerprint is provided. The method is useful for generating data for use in various processes concerned with fingerprints and particularly avoids the need to manually generate and collect such data. The method includes obtaining a plurality of representations from an individual, the representations being subject to different distortions relative to one another. A function, such as a thin plate spline function, is then used to describe the effects of the different distortions on the plurality of representations obtained. This generic model of the effects of distortion can then be used to generate distortions for a further representation from an individual, preferably another individual. The simulated distorted representations can be used in a variety of ways.

This application is a Continuation application of Ser. No. 11/084,356,filed Mar. 18, 2005, which claims benefit of Serial No. 0502849.3, filedFeb. 11, 2005 in the UK, and which also claims benefit of Serial No.0423648.5, filed Oct. 26, 2004 in the UK, and which applications areincorporated herein by reference. To the extent appropriate, a claim ofpriority is made to each of the above disclosed applications.

BACKGROUND OF THE INVENTION

This invention concerns improvements in and relating to comparisons,particularly, but not exclusively to comparisons of biometric markersand the accounting for distortion involved therein.

Various approaches for comparing a biometric marker, such as afingerprint, from one source with one from another source exist. Somesuch systems have attempted to account on a case by case basis for theeffects of distortion.

SUMMARY OF THE INVENTION

The applicant has developed a likelihood ratio based approach for such acomparison and this takes into account the variation in representationsof the same finger taken under different conditions.

The present invention has amongst its aims to provide additional datafor such a process, without undue burden in its generation.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 shows a diagram of an exemplary method of simulating the effectof distortion on a representation of a marker.

DETAILED DESCRIPTION OF THE INVENTION

According to a first aspect of the invention we provide a method ofsimulating the effect of distortion on a representation of a marker, themethod including

obtaining a plurality of representations from an individual, therepresentations being subject to different distortions relative to oneanother;

describing the effect of the different distortions on the plurality ofrepresentations using a function;

taking a further representation from an individual and preferablyanother individual, applying the function to that representation togenerate one or more simulated distorted representations.

According to a second aspect of the invention we provide a method offorming a data set including distorted representations of a marker, themethod including

obtaining a plurality of representations from an individual, therepresentations being subject to different distortions relative to oneanother;

describing the effect of the different distortions on the plurality ofrepresentations using a function;

taking a further representation from an individual, preferably anotherindividual, applying the function to that representation to generate oneor more simulated distorted representations;

adding the one or more simulated distorted representations to a dataset.

The first and/or second aspects of the invention may include any of thefeatures, options or possibilities set out elsewhere in thisapplication, including from amongst the following.

The distortion may arise from one or more factors. The factors may be orinclude the particular finger and/or the particular hand from which therepresentation arises. The factor may be or include the gender and/orprofession and/or height and/or size and/or weight and/or age of theperson from whom the representation arises. The factor may be the typeand/or material and/or shape of the substrate on which therepresentation arose.

The marker, preferably a biometric marker, may be a fingerprint, but maybe a palm print, ear print, footprint, footwear print or the like.

The plurality of representations may be obtained from the individualunder controlled conditions. The conditions may be controlled in termsof the finger used and/or substrate used and/or pressure used and/orextent of distortion used. Preferably one or more repeats of eachrepresentation are obtained. Preferably at least 2 repeats and morepreferably at least 5 repeats are obtained for each of the differentdistortions. Preferably at least 5 representations with differentdistortions are obtained from each individual. Preferably a plurality ofrepresentations are obtained from a plurality of individuals. Preferablyat least 20 individuals are used, more preferably at least 40.

The function may be or include a non-linear function. The function maybe a non-linear transformation. The function may be or include one ormore matrices. The function may be defined, at least in part, by acomparison of a pair of the representations having differentdistortions. The comparison may consider the position of one or moreminutiae in each of the representations and/or consider the position ofone or more points on one or more ridges. The function may be defined,at least in part, by a thin plate spline approach.

Preferably the method is applied to a plurality of different individualsto provide a plurality of functions. One or more of the functions may beused to generate the simulated distorted representations. One or more ofthe functions may be combined, for instance to give a compositefunction. One or more of the functions may be combined to give a generaldescription of distortion. The composite function may be a compositematrix. The plurality of functions and/or composite function and/orcomposite matrix may be used to generate one or more simulated distortedrepresentations from a further representation.

The further representation to which the function is applied ispreferably an undistorted representation. The representation to whichthe function is applied may be from a different individual to theindividual or individuals that the distorted representations areobtained from. Preferably a plurality of simulated distortedrepresentations are obtained from each representation, potentially nineor more, preferably 10 or more, ideally 25 or more. The function may beused to generate one or more simulated distorted representations for aplurality of individuals, ideally with the same function being used infor each individual.

Preferably the simulated distorted representations are supplied to adata set, ideally a data base. Preferably the data set and/or data baseis used in a comparison method, particularly a comparison method inwhich a representation being compared is considered against withinfinger variability and/or between finger variability. The data setand/or data base may be used to form a probability distribution, forinstance a probability distribution related to the distance betweendifferent representations of the same marker and/or a probabilitydistribution related to the distance between different representationsof different markers.

The method may be repeated for one or more different types and/ordirection of distortion. The one or more different types of distortionmay include: distortion of and/or towards one end, for instance a top,of a representation; and/or distortion of and/or towards another end,for instance a bottom, of a representation; and/or distortion of and/ortowards another end, for instance one side, of a representation; and/ordistortion of and/or towards another end, for instance another side, ofa representation.

One or more functions may be provided. One or more functions related toor specific to the finger which was the source of the representation maybe used, for instance where the finger is the thumb, first finger, indexfinger, third finger or fourth finger. One or more functions related toor specific to the hand which was the source of the representation maybe used, for instance where the hand is the right hand or left hand. Oneor more functions related to or specific to the gender of the person whowas the source of the representation may be used, for instance where thegender is male or female. One or more functions related to or specificto the size of the person who was the source of the representation maybe used, for instance in respect of one or more hyped ranges for theperson. One or more functions related to or specific to the age of theperson who was the source of the representation may be used, forinstance with respect to one or more age ranges. One or more functionsrelated to or specific to the weight of the person who was the source ofthe representation may be used, for instance with respect to one or moreweight ranges. One or more functions related to or specific to theprofession of the person who was the source of the representation may beused.

Various embodiments of the present invention will now be described, byway of example only.

The comparison of fingerprints, or other biometric markers, obtainedfrom one source with those obtained from another source is useful for avariety of purposes, including in forensic science. In the forensicscience context, the comparison may seek to suggest that arepresentation of a finger mark from a crime scene is linked to asuspect.

The applicant has conducted research and developed an approach whichseeks to evaluate the strength of the link between a crime scenerepresentation of a fingerprint and a representation of a fingerprinttaken from a suspect and to present this evidence using a likelihoodapproach. A significant issue in this approach and in other approachesto the consideration of representations of fingerprints is the issue ofdistortion.

Whilst a suspect's print taken in a controlled manner, using preferredmaterials, is fairly consistent in terms of the representation it givesbetween occasions, this is not the case in crime scene cases.Representations of fingerprints left during day to day activities,including those which are then associated with a crime, arise under awide variety of conditions. The pressure applied, movement duringapplication, the substrate involved and a variety of other factors canall alter the form of the representation which arises when compared withothers left or with representations taken under controlled conditions.

In the approach taken by the applicant, detailed in applicant's UKpatent application number GB0422784.9 filed 14 Oct. 2004 and/or UKpatent application number GB 0502900.4 filed 11 Feb. 2005, therepresentations of interest are considered in the context of two datasets. A data set representative of the variation in representations offingerprints across the population (say based on 2000 fingerprints) anda data set representative of the variation in representations of thesame fingerprint with specific distortion are used. The existing dataset representative of the variation in the representations of the samefingerprint with distortion has been compiled by taking a fingerprintfrom a small number of individuals (say 4) and obtaining a number ofrepresentations for them under a number of specific different conditions(say 9) with a number of repeats for each (say 5). In order to ensurethat the different individuals are considered under the same variationsin conditions, an extremely time consuming and rigorous procedure isfollowed. In practical terms this limits the number of differentindividuals and number of different conditions for each which can beconsidered.

Instead of physically sampling a large number of individuals, undervarious conditions and with repeats thereof, the alternative approach ofthe present invention simulates a large number of specific distortedrepresentations from an undistorted representation. The undistortedrepresentation is easy to collect or could even be obtained from one ofa number of existing data sets of such representations. The actualgeneration of the specific distorted representations is performed by acomputer and so is quick to perform on a large scale. The simulation isrepeated on a large number of undistorted representations.

Using such an approach, the data set representative of the variation inrepresentations of the same fingerprint with distortion can be increasedsubstantially in size with only a reasonable input effort. This meansthat the approach and statistical models which use this data set aremore robust as a result, as more extensive testing and validation ispossible. An additional benefit comes from the approach enabling thecreation of very large data sets of distorted representations withoutthe need for physical sampling. A powerful research resource results.

To be able to distort undistorted representations in an appropriate way,it is necessary to derive an appropriate description of the distortionprocess. To do this, the approach involves an initial investment infurther physical representations of distortion. A significant number ofindividuals, for instance 40, are used to provide a significant numberof distorted representations of their fingerprints, for instance 50each. For each individual,

their representations and the distortion of them are then describedusing a non-linear mathematical transformation. Such an approach is moreaccurate than some prior approaches as the nature of the distortionitself is non-linear. In the preferred form the approach establishes amatrix which describes the distortion. An example of such a matrixdescription of distortion is to be found in Ross et al., Proceedings ofthe International Conference on Biometric Authentication (ICBA) HongKong, July 2004 “Estimating Fingerprint Deformation” the contents ofwhich are incorporated herein by reference.

Starting with a pair of representations, these are presented in a blackand white format, preferably skeletonised and subjected to appropriatecleaning and healing of the representation. The minutiae locations arethen determined and information on them collected for eachrepresentation using a suitable information format. The location in therepresentation and orientation of the associated ridge and grayscaleintensity of pixels in the vicinity may be captured in this way. Thedegree of correspondence between minutiae in the two representations canthen be obtained and quantified using one or more techniques, such as anelastic stringer matcher. Ridge curves can be extended from these pointsand the degree of correspondence between points on the curvesestablished too.

The global effect of different distortions between the differentrepresentations on these points is then considered. The Thin PlateSpline approach describes the dependence of point positions on a thinmetal plate with the physical bending energy applied to the thin metalplate. The Thin Plate Spline approach is a parametric generalisationfrom rigid to mild non-rigid deformations. The parameters of the ThinPlate Spline approach can be obtained from a matrix equation and variousapproaches to the solution of the equation can be taken. An averagedeformation model can be obtained from the technique.

In the Ross et al., paper, a number of representations of a marker of aparticular individual are taken. These are taken under generally similarbut uncontrolled conditions and so reflect the common extent ofvariation for that marker of that individual. The results are used toform the average deformation model for that individual. The averagedeformation model can be considered as modelling the behaviour of theindividual. The average deformation model is used to distort therepresentation or “baseline impression” of a particular individualbefore that is compared with the other, template representation of aparticular individual. As a result, the comparison process is improved.No use of the distorted representation is made outside of the onerepresentation versus another representation comparison for a particularindividual. If another individual is to be considered, thenrepresentations must be collected for him, an average deformation modelfor that individual must be generated and that individual's own averagedeformation model is used in any comparison. Each model is individualspecific, therefore, and the model for one individual may be verydifferent to the model for another.

In contrast, the present approach uses the description of specificdistortion provided by the matrix and takes it in an alternativedirection. Firstly, it differs in terms of the end use as that is totake undistorted representations, which are not involved in anyauthentication process, and deliberately convert them to distortedrepresentations. These representations are then used together with othersuch distorted representations to form a data-set, and ideally tocontribute to or validate the data set or probability distribution usedin the technique of GB0422784.9 filed 14 Oct. 2004 and/or GB0502900.4filed 11 Feb. 2005. This is a use and interest not involved in the Rosset al., process. Secondly, the approach differs because the matrixarrived at for specific distortion of an individual is consideredtogether with the matrices arrived at from corresponding distortions ofa number of other individuals so as to provide a composite matrixdescriptive of distortion in a more general sense. The model ofdeformation is not specific to an individual, therefore, but instead isapplicable between individuals. The modelling of distortion according tothe invention can address distortion as a whole, but more preferably anumber of different models to cover different directions of distortionare generated. For instance, a model for distortion of the top of therepresentation can be determined and/or a model for distortion to oneside and/or another and/or the bottom can be determined. The models canbe used individually and/or together.

The composite matrix which results provides a detailed and appropriateexpression of how specific distortion alters representations in general.As such, it is then possible to take an undistorted representation froman individual, who has not provided distorted representations which havebeen physically collected and considered, and simulate a series ofdistorted representations for that representation. Repeat uses of thedistortion matrix gives repeat distorted representations. All these areuseful in terms of contributions to the data set on betweenrepresentation variability for the same finger and/or person. Theapproach can equally well be applied to a set of ten representationscollected with one representation for each finger of the person.

Whilst a number of non-linear mathematical transformations are possible,and a number of matrix based approaches are possible, the preferredmatrix form is achieved using a Thin Plate Spline approach referencedabove. Many variations on that particular way of describing thedistortion are possible, however.

Whilst the approach is described above in the context of one, preferablycomposite, matrix, it is possible to develop a range of such matriceswhich are expressions of distortion under various conditions. Thus amatrix for each gender and/or hand possible for the person from whom therepresentation arises is possible. A series of matrices, with individualmatrices for different ages of the person from whom the representationarises, is possible. A series of matrices, with individual matrices fordifferent weights of the person from whom the representation arises, ispossible. A series of matrices, with individual matrices for differentprofessions of the person from whom the representation arises, ispossible.

By way of validation, it is possible to take one or more representationsunder controlled conditions and apply the distortion matrix to them. Theresulting distorted representations can then be compared with realrepresentations obtained under a variety of conditions and hence subjectto distortion of their own.

1.-18. (canceled)
 19. A method of simulating the effect of distortion ona representation of a marker, the method comprising: a) obtaining aplurality of representations from an individual by physically samplingthat individual, the representations being subject to differentdistortions relative to one another; b) describing the effect of thedifferent distortions on a pair of representations from amongst theplurality of representations using a function; c) repeating steps a) andb) for a plurality of individuals to provide a plurality of functions;d) obtaining a composite distorting function, the composite distortingfunction being based on a combination of two or more of the plurality offunctions; e) taking a further representation from a further individualby physically sampling that further individual, said further individualbeing a different individual from the individual of step a) and any ofthe individuals of step c) and applying the composite distortingfunction to that further representation to generate one or moresimulated distorted representations using a computer implemented method;and f) repeating step e) for another further representation.
 20. Amethod according to claim 19 in which the function is or includes anon-linear function.
 21. A method according to claim 20 in which thefunction is a non-linear transformation.
 22. A method according to claim19 in which the function is or includes one or more matrices.
 23. Amethod according to claim 19 in which the representation includes one ormore minutiae, each of the one or more minutiae having a position and inwhich the comparison considers the position of one or more minutiae ineach of the representations.
 24. A method according to claim 19 in whichthe function is defined, at least in part, by a thin plate splineapproach.
 25. A method according to claim 19 in which the plurality ofrepresentations are obtained from the individual under controlledconditions.
 26. A method according to claim 25 in which therepresentations are obtained from a finger and in which the controlledconditions are controlled in terms of the finger used and/or substrateused and/or pressure used and/or extent of distortion used.
 27. A methodaccording to claim 19 in which one or more repeats of eachrepresentation are obtained.
 28. A method according to claim 19 in whichtwo or more of the functions are combined to give the distortingfunction in the form of a composite function.
 29. A method according toclaim 19 in which two or more of the functions are combined to give ageneral description of distortion.
 30. A method according to claim 28 inwhich the composite function is used to generate one or more simulateddistorted representations from the further representation.
 31. A methodaccording to claim 19 in which the further representation to which thefunction is applied is an undistorted representation.
 32. A methodaccording to claim 19 in which a plurality of simulated distortedrepresentations are obtained from each representation.
 33. A methodaccording to claim 19 in which the distorting function is used togenerate one or more simulated distorted representations for a pluralityof other individuals, with the distorting function used for each of theother individuals being the same.
 34. A method according to claim 19 inwhich the simulated distorted representations are supplied to a dataset.
 35. A method according to claim 34 in which the data set is used ina comparison method in which a representation being compared isconsidered against within finger variability and/or between fingervariability.
 36. A method according to claim 34 in which the data set isused to form a probability distribution.
 37. A method according to claim36 in which there is a distance between different representations of themarker, wherein the marker is the same in the different representationsand the probability distribution relates to the distance betweendifferent representations of the same marker and/or in which there is adistance between different representations of different markers and theprobability distribution relates to the distance between differentrepresentations of different markers.
 38. A method according to claim 19in which the method is repeated for one or more different types and/ordirections of distortion.
 39. A method of simulating the effect ofdistortion on a representation of a marker, the method including: a)obtaining a plurality of representations from an individual byphysically sampling that individual, the representations being subjectto different distortions relative to one another; b) describing theeffect of the different distortions on a pair of representations fromamongst the plurality of representations using a function; c) repeatingsteps a) and b) for a plurality of individuals to provide a plurality offunctions; d) taking two or more of the functions and combining them togive a composite function; e) taking a further representation from afurther individual by physically sampling that further individual andapplying the distorting function to that further representation togenerate one or more simulated distorted representations using acomputer implemented method, the distorting function being the compositefunction.
 40. A method of analysing a representation of a marker, themethod including 1) obtaining a representation of the marker from alocation; 2) processing the representation by applying a compositefunction to the representation to generate one or more revisedrepresentations using a computer implemented method, the compositefunction being obtained by a method including: a) obtaining a pluralityof representations from an individual by physically sampling thatindividual, the representations being subject to different distortionsrelative to one another; b) describing the effect of the differentdistortions on a pair of representations from amongst the plurality ofrepresentations using a function; c) repeating steps a) and b) for aplurality of individuals to provide a plurality of functions; and d)taking two or more of the functions of step c) and combining them togive the composite function; the method of analysis further including:3) comparing the one or more revised representations with one or moreexisting representations to analyse the representation of the marker fora match with the one or more existing representations and/or a lack of amatch with the one or more existing representations.
 41. A method ofanalysing a representation of a marker, the method including 1)obtaining a representation of the marker from a location; 2) processingthe representation by applying a composite function to therepresentation to generate one or more revised representations, thecomposite function being obtained by a method including: a) obtaining aplurality of representations from an individual by physically samplingthat individual, the representations being subject to differentdistortions relative to one another; b) describing the effect of thedifferent distortions on a pair of representations from amongst theplurality of representations using a function; and c) repeating steps a)and b) for a plurality of individuals to provide a plurality offunctions, the composite function being based on two or more theplurality of functions; the method of analysis further including: 3)comparing the one or more revised representations with one or moreexisting representations to analyse the representation of the marker fora match with the one or more existing representations and/or a lack of amatch with the one or more existing representations.
 42. A methodaccording to claim 41 in which the comparing considers a position of oneor more minutiae in each of the revised representations and the one ormore existing representation and/or considers a position of one or morepoints on one or more ridges in each of the revised representations andthe one or more existing representation.
 43. A method according to claim41 in which the function is defined, at least in part, by a thin platespline approach.
 44. A method according to claim 41 in which two or moreof the functions are combined to give a general description ofdistortion.
 45. A method according to claim 41 in which the furtherrepresentation to which the composite function is applied is anundistorted representation.
 46. A method according to claim 41 in whicha plurality of revised representations are obtained from eachrepresentation.
 47. A method according to claim 41 in which thecomposite function is used to generate one or more revisedrepresentations for a plurality of other individuals, with the compositefunction used for each of the other individuals being the same.
 48. Amethod according to claim 19 in which the representation includes one ormore points on one or more ridges, each of the one or more points havinga position and in which the comparison considers the position of one ormore points on one or more ridges.
 49. A method according to claim 23 inwhich the representation also includes one or more points on one or moreridges, each of the one or more points having a position and in whichthe comparison considers the position of one or more points on one ormore ridges.